GMAT Exam > GMAT Questions > If |3 – x| < x + 5, which of the fol...
Start Learning for Free
If |3 – x| < x + 5, which of the following may be true about x ?
I. x > –1
II. x < 2
III. x < –2
II. x < 2
III. x < –2
- a)I only
- b)II only
- c)I and II only
- d)I and III only
- e)I, II, and III
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If |3 – x| < x + 5, which of the following may be true about ...
We have the inequality |3 - x| < x + 5.
To simplify this inequality, we consider two cases:
Case 1: (3 - x) is positive or zero:
In this case, the absolute value |3 - x| can be simplified to (3 - x). Therefore, our inequality becomes (3 - x) < x + 5.
In this case, the absolute value |3 - x| can be simplified to (3 - x). Therefore, our inequality becomes (3 - x) < x + 5.
Expanding the inequality, we have:
3 - x < x + 5
3 - x < x + 5
Adding x to both sides, we get:
3 < 2x + 5
3 < 2x + 5
Subtracting 5 from both sides, we have:
-2 < 2x
-2 < 2x
Dividing both sides by 2, we obtain:
-1 < x
-1 < x
So, in this case, the statement I. x > -1 is not true. Therefore, option C: I and II only cannot be correct.
Case 2: (3 - x) is negative:
In this case, the absolute value |3 - x| can be simplified to -(3 - x), changing the direction of the inequality. Therefore, our inequality becomes -(3 - x) < x + 5.
In this case, the absolute value |3 - x| can be simplified to -(3 - x), changing the direction of the inequality. Therefore, our inequality becomes -(3 - x) < x + 5.
Expanding the inequality and simplifying, we have:
-x + 3 < x + 5
-x + 3 < x + 5
Adding x to both sides, we get:
3 < 2x + 5
3 < 2x + 5
Subtracting 5 from both sides, we have:
-2 < 2x
-2 < 2x
Dividing both sides by 2, we obtain:
-1 < x
-1 < x
So, in this case, the statement I. x > -1 is not true. Therefore, option C: I and II only cannot be correct.
Most Upvoted Answer
If |3 – x| < x + 5, which of the following may be true about ...
Understanding the Inequality
To solve the inequality |3 - x| < x="" +="" 5,="" we="" need="" to="" consider="" two="" cases="" based="" on="" the="" definition="" of="" absolute="" />
Case 1: 3 - x ≥ 0 (i.e., x ≤ 3)
Here, |3 - x| = 3 - x. The inequality becomes:
3 - x < x="" +="" />
Rearranging gives:
3 - 5 < />
-2 < />
x > -1
Case 2: 3 - x < 0="" (i.e.,="" x="" /> 3)
In this case, |3 - x| = x - 3. The inequality transforms to:
x - 3 < x="" +="" />
This simplifies to:
-3 < 5,="" which="" is="" always="" />
Combining Results
From Case 1, we have x > -1. Since Case 2 is always true for x > 3, we need to analyze the results further.
Checking Statements
Now let's evaluate the statements:
I. x > -1
- This holds true based on Case 1.
II. x < 2="" />
- This is possible since x can range from -1 to any value less than 3. Thus, x can indeed be less than 2.
III. x < -2="" />
- This cannot be true because we established that x must be greater than -1.
Conclusion
Therefore, only Statements I and II are valid:
- I. x > -1 (True)
- II. x < 2="" />
- III. x < -2="" />
Thus, the correct answer is option 'C': I and II only.
To solve the inequality |3 - x| < x="" +="" 5,="" we="" need="" to="" consider="" two="" cases="" based="" on="" the="" definition="" of="" absolute="" />
Case 1: 3 - x ≥ 0 (i.e., x ≤ 3)
Here, |3 - x| = 3 - x. The inequality becomes:
3 - x < x="" +="" />
Rearranging gives:
3 - 5 < />
-2 < />
x > -1
Case 2: 3 - x < 0="" (i.e.,="" x="" /> 3)
In this case, |3 - x| = x - 3. The inequality transforms to:
x - 3 < x="" +="" />
This simplifies to:
-3 < 5,="" which="" is="" always="" />
Combining Results
From Case 1, we have x > -1. Since Case 2 is always true for x > 3, we need to analyze the results further.
Checking Statements
Now let's evaluate the statements:
I. x > -1
- This holds true based on Case 1.
II. x < 2="" />
- This is possible since x can range from -1 to any value less than 3. Thus, x can indeed be less than 2.
III. x < -2="" />
- This cannot be true because we established that x must be greater than -1.
Conclusion
Therefore, only Statements I and II are valid:
- I. x > -1 (True)
- II. x < 2="" />
- III. x < -2="" />
Thus, the correct answer is option 'C': I and II only.
Free Test
FREE
| Start Free Test |
Community Answer
If |3 – x| < x + 5, which of the following may be true about ...
We have the inequality |3 - x| < x + 5.
To simplify this inequality, we consider two cases:
Case 1: (3 - x) is positive or zero:
In this case, the absolute value |3 - x| can be simplified to (3 - x). Therefore, our inequality becomes (3 - x) < x + 5.
In this case, the absolute value |3 - x| can be simplified to (3 - x). Therefore, our inequality becomes (3 - x) < x + 5.
Expanding the inequality, we have:
3 - x < x + 5
3 - x < x + 5
Adding x to both sides, we get:
3 < 2x + 5
3 < 2x + 5
Subtracting 5 from both sides, we have:
-2 < 2x
-2 < 2x
Dividing both sides by 2, we obtain:
-1 < x
-1 < x
So, in this case, the statement I. x > -1 is not true. Therefore, option C: I and II only cannot be correct.
Case 2: (3 - x) is negative:
In this case, the absolute value |3 - x| can be simplified to -(3 - x), changing the direction of the inequality. Therefore, our inequality becomes -(3 - x) < x + 5.
In this case, the absolute value |3 - x| can be simplified to -(3 - x), changing the direction of the inequality. Therefore, our inequality becomes -(3 - x) < x + 5.
Expanding the inequality and simplifying, we have:
-x + 3 < x + 5
-x + 3 < x + 5
Adding x to both sides, we get:
3 < 2x + 5
3 < 2x + 5
Subtracting 5 from both sides, we have:
-2 < 2x
-2 < 2x
Dividing both sides by 2, we obtain:
-1 < x
-1 < x
So, in this case, the statement I. x > -1 is not true. Therefore, option C: I and II only cannot be correct.
|
Explore Courses for GMAT exam
|
|
Top Courses for GMATView all
If |3 – x| < x + 5, which of the following may be true about x ?I. x > –1II. x < 2III. x < –2a)I onlyb)II onlyc)I and II onlyd)I and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer?
Question Description
If |3 – x| < x + 5, which of the following may be true about x ?I. x > –1II. x < 2III. x < –2a)I onlyb)II onlyc)I and II onlyd)I and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If |3 – x| < x + 5, which of the following may be true about x ?I. x > –1II. x < 2III. x < –2a)I onlyb)II onlyc)I and II onlyd)I and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If |3 – x| < x + 5, which of the following may be true about x ?I. x > –1II. x < 2III. x < –2a)I onlyb)II onlyc)I and II onlyd)I and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer?.
If |3 – x| < x + 5, which of the following may be true about x ?I. x > –1II. x < 2III. x < –2a)I onlyb)II onlyc)I and II onlyd)I and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If |3 – x| < x + 5, which of the following may be true about x ?I. x > –1II. x < 2III. x < –2a)I onlyb)II onlyc)I and II onlyd)I and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If |3 – x| < x + 5, which of the following may be true about x ?I. x > –1II. x < 2III. x < –2a)I onlyb)II onlyc)I and II onlyd)I and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer?.
Solutions for If |3 – x| < x + 5, which of the following may be true about x ?I. x > –1II. x < 2III. x < –2a)I onlyb)II onlyc)I and II onlyd)I and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of If |3 – x| < x + 5, which of the following may be true about x ?I. x > –1II. x < 2III. x < –2a)I onlyb)II onlyc)I and II onlyd)I and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If |3 – x| < x + 5, which of the following may be true about x ?I. x > –1II. x < 2III. x < –2a)I onlyb)II onlyc)I and II onlyd)I and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer?, a detailed solution for If |3 – x| < x + 5, which of the following may be true about x ?I. x > –1II. x < 2III. x < –2a)I onlyb)II onlyc)I and II onlyd)I and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of If |3 – x| < x + 5, which of the following may be true about x ?I. x > –1II. x < 2III. x < –2a)I onlyb)II onlyc)I and II onlyd)I and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If |3 – x| < x + 5, which of the following may be true about x ?I. x > –1II. x < 2III. x < –2a)I onlyb)II onlyc)I and II onlyd)I and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup